Geometry and measures worksheet — GCSE Foundation

1.A perpendicular bisector is drawn through the midpoint of a line segment AB. Which set of points does this construction show?

2.A solid has 5 faces, 9 edges and 6 vertices. Two of its faces are triangles and the other three are rectangles. Which solid is it?

3.Each of these has an exact value. Write down the one whose value is the greatest.

4.A solid pyramid has a square base of side 10 cm and four identical triangular faces. Its apex is directly above the centre of the base, at a vertical height of 12 cm, and the slant height of each triangular face — the distance from the apex to the midpoint of a base edge — is 13 cm. Work out the total surface area of the pyramid.

5.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.

6.Rectangle ABCD has vertices A(−1, 2), B(4, 2), C(4, 5) and D(−1, 5). The rectangle is translated so that C moves to (0, −1). Write down the coordinates of the image of A.

7.A straight line touches the edge of a circle at exactly one point and does not cross into the circle at all. Write down the term for this line.

8.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.

9.A garden plan is drawn to a scale of 1 cm : 1.8 m. A path on the plan measures 4.5 cm. What is the real length of the path, in metres, to 1 decimal place?

10.A sector of a circle has radius 15 cm and angle 216°. Using π = 3.14, work out the arc length of the sector.

11.A square-based pyramid is cut by a flat plane parallel to its base, partway up between the base and the apex. What shape is the cross-section?

12.How many vertices does a square-based pyramid have?

13.A rectangular photograph is 12 cm long and 5 cm wide. Work out the perimeter of the photograph.

14.Which of these correctly compares a 'line' with a 'line segment'?

15.A cuboid has a length, width and height that are all different from each other. How many planes of symmetry does it have?